Is there a way to output gif animation from blender?
No, there isn't a way to export (or import) gif directly.
GIF is not a supported format in blender.
You would need to export your images or animation in a different format, and then convert it to GIF using an external application.
For a list of the supported formats read this.
To record a screen capture using external software refer to this post in Meta:
What is the process for creating gifs for questions and answers?